相关论文: Parametric Level Correlations in Random-Matrix Mod…

The permutation symmetry of neurons in each layer of a deep neural network gives rise not only to multiple equivalent global minima of the loss function, but also to first-order saddle points located on the path between the global minima.…

In this paper we analyze a quartic tensor model with one interaction for a tensor of arbitrary rank. This model has a critical point where a continuous limit of infinitely refined random geometries is reached. We show that the critical…

This paper summarizes some work I've been doing on eigenvalue correlators of Random Matrix Models which show some interesting behaviour. First we consider matrix models with gaps in there spectrum or density of eigenvalues. The…

We study symmetry breaking in $Z_2$ symmetric large $N$ matrix models. In the planar approximation for both the symmetric double-well $\phi^4$ model and the symmetric Penner model, we find there is an infinite family of broken symmetry…

The effect of disorder on the perpendicular magnetoresistance of magnetic multilayers is investigated theoretically. Various kinds of disorder are considered: (i) interface substitutional disorder and (ii) bulk disorder in the various…

This article is dedicated to the following class of problems. Start with an $N\times N$ Hermitian matrix randomly picked from a matrix ensemble - the reference matrix. Applying a rank-$t$ perturbation to it, with $t$ taking the values $1\le…

This paper rigorously shows how over-parameterization changes the convergence behaviors of gradient descent (GD) for the matrix sensing problem, where the goal is to recover an unknown low-rank ground-truth matrix from near-isotropic linear…

We consider interacting paraparticle chains with a constant $R$-matrix where the Hamiltonian sums over the internal degrees (flavors) of the paraparticles. For such flavor-blind Hamiltonians we show a general factorization of the Hilbert…

The mobility of two interacting particles in a random potential is studied, using the sensitivity of their levels to a change of boundary conditions. The delocalization in Hilbert space induced by the interaction of the two particle Fock…

We report an instability exhibited by a fluid system when coupling two distinct types of waves, both linearly damped. While none of them is unstable on its own, they amplify one another, resulting in a previously unreported convective…

In two-dimensional lattice fermion model a determinant representation for the two-point correlation function of the twist field in the disorder phase is obtained. This field is defined by twisted boundary conditions for lattice fermion…

We investigate the synchronization features of a network of spiking neurons under a distance-dependent coupling following a power-law model. The interplay between topology and coupling strength leads to the existence of different…

We consider level crossing in a matrix family $H=H_0+\lambda V$ where $H_0$ is a fixed $N\times N$ matrix and $V$ belongs to one of the standard Gaussian random matrix ensembles. We study the probability distribution of level crossing…

The frustrated ladder with alternate ferromagnetic(F) exchange $-J_F$ and AF exchange $J_A$ to first neighbors and F exchange $-J_L$ to second neighbors is studied by exact diagonalization (ED) and density matrix renormalization group…

We present useful connections between the finite difference and the finite element methods for a model boundary value problem. We start from the observation that, in the finite element context, the interpolant of the solution in one…

Robust and semiparametric statistics are of the same historical origin and largely employ the same locally asymptotically normal framework. In our talk, we consider he following more intrinsic connections of both fields: 1) Robust influence…

The spontaneous symmetry breaking at zero temperature in the four-component four-dimensional scalar $\lambda \phi^4_4$ model (the O(4) model) is investigated on a lattice for different values of the coupling constant $\lambda$. A general…

We present explicitly a relation between the Nambu-Goldstone boson and the order parameter in non-relativistic systems with spontaneous symmetry breaking. We show that the Nambu-Goldstone bosons are characterized by transformation property…

Macroscopic loop correlators are investigated in the hermitian one matrix model with the potential perturbed by the higher order curvature term. In the phase of smooth surfaces the model is equivalent to the minimal conformal matter coupled…

We describe the large-time moment asymptotics for the parabolic Anderson model where the speed of the diffusion is coupled with time, inducing an acceleration or deceleration. We find a lower critical scale, below which the mass flow gets…